While I'm aware of the fact that causality implies that the present output is only dependent on present and past inputs, something that is bugging me is what if the input is dependent on future outputs. Would the system be causal or anti-causal in that case? I look at this with the assumption that since input depends on the future outputs, then in that case, the outputs only ever depend on the past and present inputs and thus should be causal. I would love some insight into this. Take, for example:$x[n]=y[n-1]-2.5y[n]+y[n+1]$where $x[n]$& $y[n]$ are inputs and outputs of an LTI system, respectively.
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